The Republican’s resignation as secretary of state follows calls by Ms. Abrams and others to step down so he wouldn’t oversee an election in which he was a candidate

ATLANTA—Republican Brian Kemp, the self-declared winner of Georgia’s contentious gubernatorial election, announced Thursday he was resigning as secretary of state to focus on the transition to his new office.

“After receiving the highest number of votes of any gubernatorial candidate in state history, Governor-elect Kemp will focus full-time on a successful transition,” Mr. Kemp’s spokesman Ryan Mahoney said.